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Chapter 3: Problem 103

A mixture of \(\mathrm{N}_{2}(g)\) and \(\mathrm{H}_{2}(g)\) reacts in a closed container to form ammonia, \(\mathrm{NH}_{3}(g) .\) The reaction ceases before either reactant has been totally consumed. At this stage \(3.0 \mathrm{mol} \mathrm{N}_{2}, 3.0 \mathrm{mol} \mathrm{H}_{2},\) and 3.0 \(\mathrm{mol} \mathrm{NH}_{3}\) are present. How many moles of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) were present originally?

Short Answer

Expert verified
There were originally 4.5 moles of \(N_{2}\) and 7.5 moles of \(H_{2}\) present in the container.

Step by step solution

01

Write the balanced chemical equation

The balanced chemical equation for the formation of ammonia is: \[N_{2}(g) + 3H_{2}(g) \rightarrow 2NH_{3}(g)\]
02

Calculate moles of N2 and H2 consumed in the reaction

As 3.0 mol NH3 is formed, we can use stoichiometry to determine the moles of N2 and H2 consumed in the reaction. \[\frac{\text{moles of } N_{2}}{\text{moles of } H_{2}} = \frac{1}{3}\] From the balanced equation, we know that \(1 \ mol \ of \ N_{2} \) reacts with \(3 \ mol \ of \ H_{2}\) to produce \(2 \ mol \ of \ NH_{3}\). Therefore, \[\frac{x}{3x} = \frac{1}{3}\] Since we have 3.0 mol of NH3 at equilibrium, we can use stoichiometry to find the moles of N2 and H2 that reacted. \[\frac{x}{3x} = \frac{\text{moles of } N_{2}}{\text{moles of } H_{2}} = \frac{1}{3} \Rightarrow x = 1.5\] So, 1.5 mol of N2 and 4.5 mol of H2 were consumed in the reaction.
03

Determine the original moles

Now that we know how many moles of N2 and H2 were consumed, we can find the original moles when the reaction reaches equilibrium: Original moles of N2 = Moles of N2 at equilibrium + Moles of N2 consumed in the reaction Original moles of N2 = 3.0 mol + 1.5 mol = 4.5 mol Original moles of H2 = Moles of H2 at equilibrium + Moles of H2 consumed in the reaction Original moles of H2 = 3.0 mol + 4.5 mol = 7.5 mol So, there were originally 4.5 moles of N2 and 7.5 moles of H2 present in the container.

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Most popular questions from this chapter

A compound, \(\mathrm{KBrO}_{x},\) where \(x\) is unknown, is analyzed and found to contain 52.92\(\%\) Br. What is the value of \(x ?\)

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(a) Write "true" or "false" for each statement. (a) A mole of horses contain a mole of horse legs. (b) A mole of water has a mass of 18.0 \(\mathrm{g} .\) (c) The mass of 1 molecule of water is 18.0 \(\mathrm{g}\) (d) A mole of NaCl (s) contains 2 moles of ions.
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